Structuring Numbers 1 to 20: Developing Facile Addition and Subtraction

David Ellemor-Collins & Robert (Bob) Wright, Southern Cross University

The purpose of this paper is to formulate students’ development toward facile addition and subtraction as an activity of structuring numbers. We aim to articulate the activity of structuring numbers, and how it can result in significant advancement in students’ arithmetical knowledge. Such an analysis can in turn inform our refinement of the instructional design.

The Numeracy Intervention Research Project (NIRP) aims to develop assessment and instructional tools for use with low-attaining 3rd- and 4thgraders. The NIRP approach to instruction in addition and subtraction in the range 1 to 20 is described. The approach is based on a notion of structuring numbers, which draws on the work of Freudenthal and the Realistic Mathematics Education program. NIRP involved 25 teachers and 300 students, 200 of whom participated in an intervention program of
approximately thirty 25-minute lessons over 10 weeks. Data is drawn from case studies of two intervention students who made significant progress toward facile addition and subtraction. Pre- and post-assessment interviews and five lesson episodes are described, and data drawn from the activity of
the students during the episodes are analysed. The discussion develops a detailed account of the progression of students’ learning of structuring numbers, and how this can result in significant level-raising of students’ arithmetical knowledge as it becomes more formalised and less context dependent.